Higher June 2019 Paper 2 Q10
10 \(x\) is an integer.
\[\begin{gathered} -4 < x \leqslant 2 \\ \text{and} \\ 2 \leqslant x + 3 < 9 \end{gathered}\]Work out all the possible values of \(x\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(-1 \quad 0 \quad 1 \quad 2\) | B3 | B2 three correct values with no incorrect values or \(-3 \quad {-2} \quad {-1} \quad 0 \quad 1 \quad 2\) and \(-1 \quad 0 \quad 1 \quad 2 \quad 3 \quad 4 \quad 5\) or interval that contains only the integers \(-1 \quad 0 \quad 1 \quad 2\) B1 \(-3 \quad {-2} \quad {-1} \quad 0 \quad 1 \quad 2\) or \(-1 \quad 0 \quad 1 \quad 2 \quad 3 \quad 4 \quad 5\) SC2 answer \(2 \quad 3 \quad 4 \quad 5\) |
Additional guidance
| Examples of intervals that contain only the integers \(-1 \quad 0 \quad 1 \quad 2\) \(-1 \leqslant x \leqslant 2\) or \([-1, 2]\) or \(-2 < x < 3\) or \((-2, 3)\) | |
| \(-1 \quad 0 \quad 1 \quad 2 \quad 3 \quad 4 \quad 5\) may be shown as an interval that contains only these integers eg \(-1 \leqslant x < 6\) or \([-1, 6)\) | |
| Intervals can be shown on a number line | |
| \(-3 \quad {-2} \quad {-1} \quad 0 \quad 1 \quad 2\) can not be shown as an interval or on a number line | |
| Lists may be in any order eg \(1 \quad 2 \quad 3 \quad 4 \quad 5 \quad {-1} \quad 0\) | B1 |
| Condone repeats in lists eg \(-1 \quad 0 \quad 1 \quad 1 \quad 2\) | B3 |
| Ignore commas/and/or between numbers in lists | |
| \(-3 \quad {-2} \quad {-1} \quad 0 \quad 1 \quad 2 \quad 3 \quad 4 \quad 5\) with no other valid working | B0 |